Find the volume $V$ of a cone if diameter $d = 6 cm$ and slant height $l = 5 cm$ .

Answer

$16 π cm^{3}$

Explanation

STEP 1: find radius $r$

To find radius $r$ use formula:

d = 2 \cdot r

After substituting $d = 6 cm$ we have:

6 cm = 2 \cdot r

r = \frac{6 cm}{2}

r = 3 cm

STEP 2: find side $h$

To find side $h$ use Pythagorean Theorem:

r^{2} + h^{2} = l^{2}

After substituting $r = 3 cm$ and $l = 5 cm$ we have:

(3 cm)^{2} + h^{2} = (5 cm)^{2}

h^{2} = (5 cm)^{2} - (3 cm)^{2}

h^{2} = 25 cm^{2} - 9 cm^{2}

h^{2} = 16 cm^{2}

h = 16 cm^{2}

h = 4 cm

STEP 3: find volume $V$

To find volume $V$ use formula:

V = \frac{h ^{2} \cdot r \cdot π}{3}

After substituting $r = 3 cm$ and $h = 4 cm$ we have:

V = \frac{16 cm ^{2} \cdot 3 cm \cdot π}{3}

V = \frac{48 cm ^{3} π}{3}

V = 16 π cm^{3}

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Find the volume V of a cone if diameter d=6cm and slant height l=5cm.

16πcm3

Find the volume $V$ of a cone if diameter $d = 6 cm$ and slant height $l = 5 cm$ .

$16 π cm^{3}$